Good things come to those who wait. And yet it seems they also come to those who flail around wildly looking for the nearest handhold, regularly hurl the last six months of forward planning out of the window, and generally don't seem to be able to sit down for any period of time without jabbing themselves in the foot with the nearest sharp implement. For Sunderland, progress to Sunday's Capital One Cup final has involved not so much a cup run as a compelling kind of cup stampede, fraught with hierarchal change, a fast-paced turnover in playing staff and the continual clank-clank of gear-shift and about-turn.

Not that there is anything new in any of this. It is now four years since Ellis Short bought the club from the Drumaville Consortium, during which time Short's bafflingly incontinent administration has signed 42 players and sold 53, including 14 new signings from 10 different leagues in the past year alone. Four permanent managers have come and gone, along with three temporary ones, a disgruntled-looking Roy Keane, one fascism-related scandal, an improbable ginger-bearded director of football, and at least £200m of Short's own money in transfers and wages. From a distance the American private equity tycoon with a personal fortune of $3bn seems the most unlikely of accidental cup finalists, a man who has effectively blundered his way to Wembley in the past six months.

As ever in football the truth is a little less straightforward. Sunderland's mistakes have been obvious enough, given a sharper focus of late by a disastrous summer transfer window, the sacking of Paolo Di Canio and the departure in January of Roberto De Fanti, a personal acquaintance of Short appointed director of football last year who oversaw a string of hapless new signings.

Even now Sunderland's administration looks oddly callow and homemade, with only Short, a man who knows a great deal about money and a proportionately small amount about elite-level football in any coherent advisory capacity, and the chief executive, Margaret Byrne, above the manager, Gus Poyet.

In spite of which these mercurial Black Cats are currently halfway to performing a mid-air pirouette and landing back on their feet. Should Poyet's team beat Manchester City at Wembley and then, on the back of some encouraging recent momentum, edge themselves from 18th to 17th in the Premier League table in the next six weeks, a season that has at times seemed on the verge of meltdown could end up as one of the most memorable in Sunderland's postwar history.

Yet even within sight of an unlikely good news story there are still contradictions. The League Cup final itself arrives as a mixed mid-season blessing. Such have been the travails of recent winners it is even tempting to talk about the Curse of the Capital One. The holders, Swansea, won just one of their final 10 Premier League matches last season and have since sacked Michael Laudrup. Kenny Dalglish was sacked three months after winning it in 2012. Birmingham won it in 2011 and were relegated the same season. Spurs won it in 2008 and sacked Juande Ramos the same year. Chelsea won it under José Mourinho the year before that and were being managed by Avram Grant within six months.

For Sunderland the fear is naturally that success at Wembley might induce a release of tension at a vital stage in the Premier League season. And yet this in turn raises a broader question, the wider issue of what, exactly, the likes of Short are in this for anyway. Why do they do it, these otherwise rather sober entrepreneur-owners, stakeholders in what is a horribly fraught and emotive business?

It is tempting to compare owning a Premier League football club to owning an airline, a confusingly multifarious business that is on the face of it as much about prestige and status as any sensible notions of money-making. Sunderland's opponents at Wembley, Manchester City, have spent close to £1bn, with a return so far of a single FA Cup and that breathless last-day league title two years ago.

At Aston Villa Randy Lerner has consistently lost money, last year writing off loan repayments worth £20m. Liverpool's debt continues to rise, if not uncontrollably. And yet, as Short has discovered, owning a football club can also feel a bit like owning a house during a boom in the market. Sometimes no matter what you do to it, how many ill-fated schemes you set out on, how may walls you tear down and leave unfinished, it still just keeps on going up in value.

For all the lows of the last year a place in the Premier League remains a guarantee of hugely increased television revenues and ramped up shirt sponsorship deals. Helped by some chaotically productive wheeler dealing, and the Stadium of Light's second life as a concert venue for the likes of Coldplay and Bruce Springsteen, Sunderland managed to rake in £96.4m in total revenues last year, more than the Turkish champions, Galatasaray.

Against this, £100,000 for winning the Capital One Cup looks like small beer, as does the promised interference of a turn in the Europa League. Albeit, again the question of exactly what top-level football is for these days raises its head.

Short is the most hard-nosed of operators in his financial career, but there is a creeping, familiar sense – this is after all, English football – of a chairman who does at times seem to enjoy the high visibility benefits of life as a Premier League chairman, who separately owns the Scottish celebrity haunt Skibo Castle, revels in his face-to-face encounters with Sunderland's fans, and who was recently in the news for leaving a £1,800 tip while dining out in a city centre curry house after the win over Everton.

Not that Short does not deserve to enjoy himself a little after the rigours of early season. In particular the appointment of Poyet has been a clear success so far, an indication once again of how in football one good decision can draw a veil over a bucket-load of wrong turns. Sunderland's manager has this week gone from saying he would always choose Premier League survival over winning the League Cup to a state of obvious excitement ahead of Sunday's final.

Short was something of a lone cheerleader for Poyet before his appointment, but the Uruguayan's energy, his commitment to the club, and a run of recent victories have threatened to recalibrate Sunderland's season: post-Wembley they have six winnable home matches in the league, to go alongside away games at Liverpool, Spurs, Chelsea and Manchester United.

If victory against City's heavyweights remains an unlikely prospect, Sunderland have won four and drawn two of the last eight matches between the two, and lost just once in the last five. They have a goalkeeper in fine form, a former City winger in Adam Johnson with seven goals in his last nine matches and opponents who might, just, have their eyes set on broader horizons.

For all that, this is still Sunderland, a club apparently set this season on taking the path of most resistance. One thing seems certain. It is unlikely to be dull.